Yes, I just created a Kha project and compiled it immediately (for Windows, not Windows Universal). It works fine in HTML5, both debug and release. A blank (black) window pops up no problem when I run it.
I also tried reverting Kode to use its own version of Kha, and that also seems to work now, although it can't compile only because I didn't install the SDK version it requires. I'll try that one later to see what happens.
About the script errors, I just noticed they're VS related, and probably irrelevant. The same error dialogue boxes popped up when I closed the solution, and they also pop up when I debug a simple Desktop Application (not Kha related). I did that as you suggested earlier, to test if I could create and build a Desktop App, and it worked fine; compiled and ran no problem at all. So I'm guessing the script errors are related to certain web-like elements in VS, both in the diagnostic tools and its "Start Page". As you can see in my previous screenshot, there's a white blank area in the diagnostic tools panel, which shouldn't be blank. I didn't edit that out, it's really looking like that. I had noticed this on VS2015 before, but VS2015 told me to install an updated version of Internet Explorer in order for it to be able to display some information there. I couldn't be bothered doing that.
But anyway, since the errors also happen when debugging an unrelated Desktop App, and that one still compiles and runs fine, I'm guessing they're actually irrelevant.